5k-9/2k=4k-1

Solution for 5k-9/2k=4k-1 equation:

5k-9/2k=4k-1

We move all terms to the left:

5k-9/2k-(4k-1)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We get rid of parentheses

5k-9/2k-4k+1=0

We multiply all the terms by the denominator


5k*2k-4k*2k+1*2k-9=0

Wy multiply elements

10k^2-8k^2+2k-9=0

We add all the numbers together, and all the variables

2k^2+2k-9=0

a = 2; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·2·(-9)
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*2}=\frac{-2-2\sqrt{19}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*2}=\frac{-2+2\sqrt{19}}{4}
$